Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation.

By considering the long-wavelength limit of the regularized long wave ~RLW! equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg–de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiplescale method in obtaining uniform perturbative series. @S1063-651X~96!08909-X#